The Stacks project

Lemma 17.30.3. Let $X$ be a topological space. Let $\mathcal{A} \to \mathcal{B}$ be a homomorphism of sheaves of rings on $X$. The differentials $\text{d} : \Omega ^ i_{\mathcal{B}/\mathcal{A}} \to \Omega ^{i + 1}_{\mathcal{B}/\mathcal{A}}$ are differential operators of order $1$.

Proof. Via our construction of the de Rham complex above as the sheafification of the rule $U \mapsto \Omega ^\bullet _{\mathcal{B}(U)/\mathcal{A}(U)}$ this follows from Algebra, Lemma 10.133.8. $\square$

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